A fast computational model for circulatory dynamics: effects of left ventricle–aorta coupling

The course of diseases such as hypertension, systolic heart failure and heart failure with a preserved ejection fraction is affected by interactions between the left ventricle (LV) and the vasculature. To study these interactions, a computationally efficient, biophysically based mathematical model for the circulatory system is presented. In a four-chamber model of the heart, the LV is represented by a previously described low-order, wall volume-preserving model that includes torsion and base-to-apex and circumferential wall shortening and lengthening, and the other chambers are represented using spherical geometries. Active and passive myocardial mechanics of all four chambers are included. The cardiac model is coupled with a wave propagation model for the aorta and a closed lumped-parameter circulation model. Parameters for the normal heart and aorta are determined by fitting to experimental data. Changes in the timing and magnitude of pulse wave reflections by the aorta are demonstrated with changes in compliance and taper of the aorta as seen in aging (decreased compliance, increased diameter and length), and resulting effects on LV pressure–volume loops and LV fiber stress and sarcomere shortening are predicted. Effects of aging of the aorta combined with reduced LV contractile force (failing heart) are examined. In the failing heart, changes in aortic properties with aging affect stroke volume and sarcomere shortening without appreciable augmentation of aortic pressure, and the reflected pressure wave contributes an increased proportion of aortic pressure.

     

Structure and torsion in the normal and situs inversus totalis cardiac left ventricle. II. Modeling cardiac adaptation to mechanical load

Mathematical models provide a suitable platform to test hypotheses on the relation between local mechanical stimuli and responses to cardiac structure and geometry. In the present model study, we tested hypothesized mechanical stimuli and responses in cardiac adaptation to mechanical load on their ability to estimate a realistic myocardial structure of the normal and situs inversus totalis (SIT) left ventricle (LV). In a cylindrical model of the LV, 1) mass was adapted in response to myofiber strain at the beginning of ejection and to global contractility (average systolic pressure), 2) cavity volume was adapted in response to fiber strain during ejection, and 3) myofiber orientations were adapted in response to myofiber strain during ejection and local misalignment between neighboring tissue parts. The model was able to generate a realistic normal LV geometry and structure. In addition, the model was also able to simulate the instigating situation in the rare SIT LV with opposite torsion and transmural courses in myofiber direction between the apex and base [Delhaas et al. (6)]. These results substantiate the importance of mechanical load in the formation and maintenance of cardiac structure and geometry. Furthermore, in the model, adapted myocardial architecture was found to be insensitive to fiber misalignment in the transmural direction, i.e., myofiber strain during ejection was sufficient to generate a realistic transmural variation in myofiber orientation. In addition, the model estimates that, despite differences in structure, global pump work and the mass of the normal and SIT LV are similar.     

Dependence of local left ventricular wall mechanics on myocardial fiber orientation: a model study.

The dependence of local left ventricular (LV) mechanics on myocardial muscle fiber orientation was investigated using a finite element model. In the model we have considered anisotropy of the active and passive components of myocardial tissue, dependence of active stress on time, strain and strain rate, activation sequence of the LV wall and aortic afterload. Muscle fiber orientation in the LV wall is quantified by the helix fiber angle, defined as the angle between the muscle fiber direction and the local circumferential direction. In a first simulation, a transmural variation of the helix fiber angle from +60 degrees at the endocardium through 0 degrees in the midwall layers to -60 degrees at the epicardium was assumed. In this simulation, at the equatorial level maximum active muscle fiber stress was found to vary from about 110 kPa in the subendocardial layers through about 30 kPa in the midwall layers to about 40 kPa in the subepicardial layers. Next, in a series of simulations, muscle fiber orientation was iteratively adapted until the spatial distribution of active muscle fiber stress was fairly homogeneous. Using a transmural course of the helix fiber angle of +60 degrees at the endocardium, +15 degrees in the midwall layers and -60 degrees at the epicardium, at the equatorial level maximum active muscle fiber stress varied from 52 kPa to 55 kPa, indicating a remarkable reduction of the stress range. Moreover, the change of muscle fiber strain with time was more similar in different parts of the LV wall than in the first simulation. It is concluded that (1) the distribution of active muscle fiber stress and muscle fiber strain across the LV wall is very sensitive to the transmural distribution of the helix fiber angle and (2) a physiological transmural distribution of the helix fiber angle can be found, at which active muscle fiber stress and muscle fiber strain are distributed approximately homogeneously across the LV wall.     

Transmural mechanics at left ventricular epicardial pacing site

Left ventricular (LV) epicardial pacing acutely reduces wall thickening at the pacing site. Because LV epicardial pacing also reduces transverse shear deformation, which is related to myocardial sheet shear, we hypothesized that impaired end-systolic wall thickening at the pacing site is due to reduction in myocardial sheet shear deformation, resulting in a reduced contribution of sheet shear to wall thickening. We also hypothesized that epicardial pacing would reverse the transmural mechanical activation sequence and thereby mitigate normal transmural deformation. To test these hypotheses, we investigated the effects of LV epicardial pacing on transmural fiber-sheet mechanics by determining three-dimensional finite deformation during normal atrioventricular conduction and LV epicardial pacing in the anterior wall of normal dog hearts in vivo. Our measurements indicate that impaired end-systolic wall thickening at the pacing site was not due to selective reduction of sheet shear, but rather resulted from overall depression of fiber-sheet deformation, and relative contributions of sheet strains to wall thickening were maintained. These findings suggest lack of effective end-systolic myocardial deformation at the pacing site, most likely because the pacing site initiates contraction significantly earlier than the rest of the ventricle. Epicardial pacing also induced reversal of the transmural mechanical activation sequence, which depressed sheet extension and wall thickening early in the cardiac cycle, whereas transverse shear and sheet shear deformation were not affected. These findings suggest that normal sheet extension and wall thickening immediately after activation may require normal transmural activation sequence, whereas sheet shear deformation may be determined by local anatomy.     

Impaired subendocardial contractile myofiber function in asymptomatic aged humans, as detected using MRI

With aging, structural and functional changes occur in the myocardium without obvious impairment of systolic left ventricular (LV) function. Transmural differences in myocardial vulnerability for these changes may result in increase of transmural inhomogeneity in contractile myofiber function. Subendocardial fibrosis and impairment of subendocardial perfusion due to hypertension might change the transmural distribution of contractile myofiber function. The ratio of LV torsion to endocardial circumferential shortening (torsion-to-shortening ratio; TSR) during systole reflects the transmural distribution of contractile myofiber function. We investigated whether the transmural distribution of systolic contractile myofiber function changes with age. Magnetic resonance tissue tagging was performed to derive LV torsion and endocardial circumferential shortening. TSR was quantified in asymptomatic young [age 23.2 (SD 2.6) yr, n = 15] and aged volunteers [age 68.8 (SD 4.4) yr, n = 16]. TSR and its standard deviation were significantly elevated in the aged group [0.47 (SD 0.12) aged vs. 0.34 (SD 0.05) young; P = 0.0004]. In the aged group, blood pressure and the ratio of LV wall mass to end-diastolic volume were mildly elevated but could not be correlated to the increase in TSR. There were no significant differences in other indexes of systolic LV function such as end-systolic volume and ejection fraction. The elevated systolic TSR in the asymptomatic aged subjects suggests that aging is associated with local loss of contractile myofiber function in the subendocardium relative to the subepicardium potentially caused by subclinical pathological incidents.     

Computational modeling of cardiac growth in the post-natal rat with a strain-based growth law

IntroductionThe postnatal heart grows mostly in response to increased hemodynamic load. However, the specific biomechanical stimuli that stimulate cardiac growth as a reaction to increased hemodynamic load are still poorly understood. It has been shown that isolated neonatal rat cardiac myocytes normalize resting sarcomere length by adding sarcomeres in series when subjected to uniaxial static strain. Because there is experimental evidence that myocytes can distinguish the direction of stretch, it was postulated that myocytes also may normalize interfilament lattice spacing as a response to cross-fiber stretch.MethodsA growth law was proposed in which fiber axial growth was stimulated by fiber strain deviating from zero and fiber radial growth by cross-fiber strain (parallel to the wall surface) deviating from zero. Fiber radial growth rate constant was 1/3 of the fiber axial growth rate constant. The growth law was implemented in a finite element model of the newborn Sprague-Dawley rat residually stressed left ventricle (LV). The LV was subjected to an end-diastolic pressure of 1 kPa and about 25 weeks of normal growth was simulated.ResultsMost cellular and chamber dimension changes in the model matched experimentally measured ones: LV cavity and wall volume increased from 2.3 and 54 μl, respectively, in the newborn to 276 μl and 1.1 ml, respectively, in the adult rat; LV shape became more spherical; internal LV radius increased faster than wall thickness; and unloaded sarcomere lengths exhibited a transmural gradient. The major discrepancy with experiments included a reversed transmural gradient of cell length in the older rat.ConclusionA novel strain-based growth law has been presented that reproduced physiological postnatal growth in the rat LV.     

Optimizing ventricular fibers: uniform strain or stress,but not ATP consumption,leads to high efficiency

The aim of this study was to investigate the influence of fiber orientation in the left ventricular (LV) wall on the ejection fraction, efficiency, and heterogeneity of the distributions of developed fiber stress, strain and ATP consumption. A finite element model of LV mechanics was used with active properties of the cardiac muscle described by the Huxley-type cross-bridge model. The computed variances of sarcomere length (SL(var)), developed stress (DS(var)), and ATP consumption (ATP(var)) have several minima at different transmural courses of helix fiber angle. We identified only one region in the used design space with high ejection fraction, high efficiency of the LV and relatively small SL(var), DS(var), and ATP(var). This region corresponds to the physiological distribution of the helix fiber angle in the LV wall. Transmural fiber angle can be predicted by minimizing SL(var) and DS(var), but not ATP(var). If ATP(var) was minimized, then the transverse fiber angle was considerably underestimated. The results suggest that ATP consumption distribution is not regulating the fiber orientation in the heart.     

Direct measurement of transmural laminar architecture in the anterolateral wall of the ovine left ventricle: new implications for wall thickening mechanics

Laminar, or sheet, architecture of the left ventricle (LV) is a structural basis for normal systolic and diastolic LV dynamics, but transmural sheet orientations remain incompletely characterized. We directly measured the transmural distribution of sheet angles in the ovine anterolateral LV wall. Ten Dorsett-hybrid sheep hearts were perfusion fixed in situ with 5% buffered glutaraldehyde at end diastole and stored in 10% formalin. Transmural blocks of myocardial tissue were excised, with the edges cut parallel to local circumferential, longitudinal, and radial axes, and sliced into 1-mm-thick sections parallel to the epicardial tangent plane from epicardium to endocardium. Mean fiber directions were determined in each section from five measurements of fiber angles. Each section was then cut transverse to the fiber direction, and five sheet angles (beta) were measured and averaged. Mean fiber angles progressed nearly linearly from -41 degrees (SD 11) at the epicardium to +42 degrees (SD 16) at the endocardium. Two families of sheets were identified at approximately +45 degrees (beta(+)) and -45 degrees (beta(-)). In the lateral region (n = 5), near the epicardium, sheets belonged to the beta(+) family; in the midwall, to the beta(-) family; and near the endocardium, to the beta(+) family. This pattern was reversed in the basal anterior region (n = 4). Sheets were uniformly beta(-) over the anterior papillary muscle (n = 2). These direct measurements of sheet angles reveal, for the first time, alternating transmural families of predominant sheet angles. This may have important implications in understanding wall mechanics in the normal and the failing heart.     

Diastolic pressure-volume relations and distribution of pressure and fiber extension across the wall of a model left ventricle.

A model for left ventricular diastolic mechanics is formulated that takes into account noneligible wall thickness, incompressibility, finite deformation, nonlinear elastic effects, and the known fiber architecture of the ventricular wall. The model consists of a hollow cylindrical mass of muscle bound between two plates of negligible mass. The wall contains fiber elements that follow a helical course and carry only axial tension. The fiber angle (i.e., helical pitch) is constant along the length of each fiber but varies through the wall in accordance with the known distribution of fiber orientations in the canine left ventricle. To simplify the analysis and reduce the number of degrees of freedom, the anatomic distribution of fiber orientations is divided into a clockwise and counterclockwise system. The reference configuration for the model corresponds to a state in which, by hypothesis, the transmural pressure gradient is zero, the tension is zero for all fibers across the wall, and all fibers are assumed to have a sarcomere length of 1.9 micrometer. This choice of reference configuration is based on the empirical evidence that canine ventricles, fixed in a state of zero transmural pressure gradient and dissected, demonstrate sarcomere lengths between 1.9 and 2.0 micrometer in inner, middle, and outer wall layers, while isolated ventricular muscle bundles are observed to have zero resting tension when the sarcomere length ranges from 1.9 to 2.0 micrometer. An equation representing the global condition for equilibrium is derived and solved numerically. It is found that the model's pressure-volume relation is representative of diastolic filling in vivo over a wide range of filling pressures, and the calculated midwall sarcomere lengths in the model compare favorably with published experimental data. Subendocardial fibers are stretched beyond Lmax even at low filling pressures, i.e., 5 mm Hg, while fibers located between 60-80% of wall thickness extend minimally between 5 and 12 mm Hg. The hydrostatic pressure field within the wall is highly nonlinear. The pressure rises steeply in the subendocardial layers so that the net gain in pressure in the inner third of the wall is 85% of the filling pressure. It is demonstrated that these results are independent of heart size for a family of heart models that are scale models of each other. They are, however, critically dependent on the existence of longitudinally oriented fibers in the endocardial and epicardial regions of heart wall.     

Differences in distensibility between the anterior and posterior walls of the left ventricle in dogs

Nonuniformity of myocardial systolic and diastolic performance in the normal left ventricle has been recognized by a number of investigators. Lack of homogeneity in diastolic properties might be caused by or related to differences in the distensibility of different regions of the left ventricular (LV) wall. Thus, we compared the end-diastolic transmural pressure-strain relations in both the anterior and posterior LV walls in seven anesthetized dogs during two interventions (pulmonary artery constriction and aortic constriction). Transmural pressure was defined as the difference between LV intracavitary pressure and local pericardial pressure. LV pressure was measured using a micromanometer; pericardial pressures over the LV anterior and posterior walls were measured with balloon transducers. Circumferentially oriented pairs of sonomicrometer crystals were implanted in the midwall of the anterior and posterior walls of the LV to measure segment lengths. Strains were calculated as (L-L0)/L0, where L was the instantaneous segment length and L0 was the segment length when transmural pressure was zero. The pattern of end-diastolic transmural pressure--strain relations was similar in all dogs. The change in strain in the posterior wall was always greater than that in the anterior wall. Opening the pericardium did not affect the difference in distensibility of the anterior and posterior walls. The results suggest that the posterior wall is more compliant than the anterior wall (that is, for a given difference in transmural pressure, the local segment length change of the posterior wall was greater). This seems consistent with other observations, which suggest that the posterior wall might make a greater contribution to diastolic filling.     

Glucosyldiacylglycerol enhances reciprocal activation of prourokinase and plasminogen

Reciprocal activation of prourokinase (pro-u-PA) and plasminogen is an important mechanism in the initiation and propagation of local fibrinolytic activity. We found that glucosyldiacylglycerol (GDG) enhanced the reciprocal activation by 1.5- to 2-fold at 0.7-16 microM, accompanying increased conversions of both zymogens to active two-chain forms. The reciprocal activation system consists of (i) plasminogen activation by pro-u-PA to form plasmin, (ii) pro-u-PA activation by the resulting plasmin to form two-chain u-PA (tcu-PA), and (iii) plasminogen activation by the resulting tcu-PA. Whereas GDG minimally affected steps (ii) and (iii) in isolated systems, it markedly enhanced step (i) in the absence of the conversion of pro-u-PA to tcu-PA. GDG significantly increased the intrinsic fluorescence of pro-u-PA (6.7%), but not that of tcu-PA or plasminogen. The large change in intrinsic fluorescence suggests that GDG selectively affects pro-u-PA to alter its conformation, and this mechanism may account for enhancement of its intrinsic plasminogen activator activity.     

Modeling ventricular repolarization: effects of transmural and apex-to-base heterogeneities in action potential durations

Heterogeneities in the densities of membrane ionic currents of myocytes cause regional variations in action potential duration (APD) at various intramural depths and along the apico-basal and circumferential directions in the left ventricle. This work extends our previous study of cartesian slabs to ventricular walls shaped as an ellipsoidal volume and including both transmural and apex-to-base APD heterogeneities. Our 3D simulation study investigates the combined effect on repolarization sequences and APD distributions of: (a) the intrinsic APD heterogeneity across the wall and along the apex-to-base direction, and (b) the electrotonic currents that modulate the APDs when myocytes are embedded in a ventricular wall with fiber rotation and orthotropic anisotropy. Our findings show that: (i) the transmural and apex-to-base heterogeneities have only a weak influence on the repolarization patterns on myocardial layers parallel to the epicardium; (ii) the patterns of APD distribution on the epicardial surface are mostly affected by the apex-to-base heterogeneities and do not reveal the APD transmural heterogeneity; (iii) the transmural heterogeneity is clearly discernible in both repolarization and APD patterns only on transmural sections; (iv) the apex-to-base heterogeneity is clearly discernible only in APD patterns on layers parallel to the epicardium. Thus, in our orthotropic ellipsoidal wall, the complex 3D electrotonic modulation of APDs does not fully mix the effects of the transmural and apex-to-base heterogeneity. The intrinsic spatial heterogeneity of the APDs is unmasked in the modulated APD patterns only in the appropriate transmural or intramural sections. These findings are independent of the stimulus location (epicardial, endocardial) and of Purkinje involvement.     

Myofiber angle distributions in the ovine left ventricle do not conform to computationally optimized predictions

Recent computational models of optimized left ventricular (LV) myofiber geometry that minimize the spatial variance in sarcomere length, stress, and ATP consumption have predicted that a midwall myofiber angle of 20 degrees and transmural myofiber angle gradient of 140 degrees from epicardium to endocardium is a functionally optimal LV myofiber geometry. In order to test the extent to which actual fiber angle distributions conform to this prediction, we measured local myofiber angles at an average of nine transmural depths in each of 32 sites (4 short-axis levels, 8 circumferentially distributed blocks in each level) in five normal ovine LVs. We found: (1) a mean midwall myofiber angle of -7 degrees (SD 9), but with spatial heterogeneity (averaging 0 degrees in the posterolateral and anterolateral wall near the papillary muscles, and -9 degrees in all other regions); and (2) an average transmural gradient of 93 degrees (SD 21), but with spatial heterogeneity (averaging a low of 51 degrees in the basal posterior sector and a high of 130 degrees in the mid-equatorial anterolateral sector). We conclude that midwall myofiber angles and transmural myofiber angle gradients in the ovine heart are regionally non-uniform and differ significantly from the predictions of present-day computationally optimized LV myofiber models. Myofiber geometry in the ovine heart may differ from other species, but model assumptions also underlie the discrepancy between experimental and computational results. To test the predictive capability of the current computational model would we propose using an ovine specific LV geometry and comparing the computed myofiber orientations to those we report herein.     

Changes in regional myocardial volume during the cardiac cycle: implications for transmural blood flow and cardiac structure

Although previous studies report a reduction in myocardial volume during systole, myocardial volume changes during the cardiac cycle have not been quantitatively analyzed with high spatiotemporal resolution. We studied the time course of myocardial volume in the anterior mid-left ventricular (LV) wall of normal canine heart in vivo (n = 14) during atrial or LV pacing using transmurally implanted markers and biplane cineradiography (8 ms/frame). During atrial pacing, there was a significant transmural gradient in maximum volume decrease (4.1, 6.8, and 10.3% at subepi, midwall, and subendo layer, respectively, P = 0.002). The rate of myocardial volume increase during diastole was 4.7 +/- 5.8, 6.8 +/- 6.1, and 10.8 +/- 7.7 ml.min(-1).g(-1), respectively, which is substantially larger than the average myocardial blood flow in the literature measured by the microsphere method (0.7-1.3 ml.min(-1).g(-1)). In the early activated region during LV pacing, myocardial volume began to decrease before the LV pressure upstroke. We conclude that the volume change is greater than would be estimated from the known average transmural blood flow. This implies the existence of blood-filled spaces within the myocardium, which could communicate with the ventricular lumen. Our data in the early activated region also suggest that myocardial volume change is caused not by the intramyocardial tissue pressure but by direct impingement of the contracting myocytes on the microvasculature.     

A two-phase finite element model of the diastolic left ventricle

A porous medium finite element model of the passive left ventricle is presented. The model is axisymmetric and allows for finite deformation, including torsion about the axis of symmetry. An anisotropic quasi-linear viscoelastic constitutive relation is implemented in the model. The model accounts for changing fibre orientation across the myocardial wall. During passive filling, the apex rotates in a clockwise direction relative to the base for an observer looking from apex to base. Within an intraventricular pressure range of 0-3 kPa the rotation angle of all nodes remained below 0.1 rad. Diastolic viscoelasticity of myocardial tissue is shown to reduce transmural differences of preload-induced sarcomere stretch and to generate residual stresses in an unloaded ventricular wall, consistent with the observation of opening angles seen when the heart is slit open. It is shown that the ventricular model stiffens following an increase of the intracoronary blood volume. At a given left ventricular volume, left ventricular pressure increases from 1.5 to 2.0 kPa when raising the intracoronary blood volume from 9 to 14 ml (100 g)-1 left ventricle.     

Left ventricular strain, rotation, and torsion as markers of acute myocardial ischemia

This study investigates how tissue Doppler imaging (TDI) and speckle tracking echocardiography (STE) describe regional myocardial deformation during controlled reductions of left anterior descending (LAD) coronary artery perfusion pressure. In eight anesthetized pigs, a shunt with constrictor was installed from the brachiocephalic artery to the LAD. Data were obtained with open shunt, followed by four degrees of stenosis (S1-S4) of increasing severity: S1, ～15%; S2, ～35%; S3, ～50%; and S4, ～60% reductions of LAD perfusion pressure. At each situation, microspheres for perfusion measurements were injected and left ventricular (LV) short- and long-axis cineloops were recorded. In the anterior wall, radial, circumferential, and longitudinal one-layer STE strain, one-layer radial TDI strain, and three-layer radial TDI and STE strain were measured. LV peak mean rotation was measured at six equidistant levels from apex to base (in 7 pigs). LV torsion was calculated from end-systolic mean rotation. With open shunt, three-layer TDI analysis showed a transmural strain gradient with no perfusion gradient. Perfusion, one-layer TDI strain, and strain in the mid- and subendocardium from three-layer TDI were reduced at S2 (P < 0.05). STE strain was not affected until S3 (P < 0.05). Peak mean rotation, increasing toward the apex, decreased at the three apical levels at S4 (P < 0.05). LV torsion did not decrease (P = 0.26). In conclusion, TDI strain detected dysfunction already with minor changes in global hemodynamics, whereas STE strain was first reduced with moderate changes. LV peak mean rotation was not reduced until severe reduction of LAD perfusion pressure, but remained increasingly counterclockwise toward the apex. LV torsion remained unaffected by ischemia.     

Acute changes of biventricular gene expression in volume and right ventricular pressure overload

OBJECTIVE: We investigated the effects of acute volume and RV pressure overload on biventricular function and gene expression of BNP, pro-inflammatory cytokines (IL-6 and TNF-alpha), iNOS, growth factors (IGF-1, ppET-1), ACE and Ca2+-handling proteins (SERCA2a, phospholamban and calsequestrin). METHODS: Male Wistar rats (n=45) instrumented with pressure tip micromanometers in right (RV) and left ventricular (LV) cavities were assigned to one of three protocols: i) Acute RV pressure overload induced by pulmonary trunk banding in order to double RV peak systolic pressure, during 120 or 360 min; ii) acute volume overload induced by dextran40 infusion (5 ml/h), during 120 or 360 min; iii) Sham. RV and LV samples were collected for mRNA quantification. RESULTS: BNP upregulation was restricted to the overloaded ventricles. TNF-alpha, IL-6, ppET-1, SERCA2a and phospholamban gene activation was higher in volume than in pressure overload. IGF-1 overexpression was similar in both types of overload, but was limited to the RV. TNF-alpha and CSQ mRNA levels were increased in the non-overloaded LV after pulmonary trunk banding. No significant changes were detected in ACE or iNOS expression. RV end-diastolic pressures positively correlated with local expression of BNP, TNF-alpha, IL-6, IGF-1, ppET-1 and SERCA2a, while RV peak systolic pressures correlated only with local expression of IL-6, IGF-1 and ppET-1. CONCLUSIONS: Acute cardiac overload alters myocardial gene expression profile, distinctly in volume and pressure overload. These changes correlate more closely with diastolic than with systolic load. Nonetheless, gene activation is also present in the non-overloaded LV of selectively RV overloaded hearts.     

Regional nonuniformity of normal adult human left ventricle

Regional nonuniformity is a feature of both diseased and normal left ventricles (LV). With the use of magnetic resonance (MR) myocardial tagging, we performed three-dimensional strain analysis on 87 healthy adults in local cardiac and fiber coordinate systems (radial, circumferential, longitudinal, and fiber strains) to characterize normal nonuniformities and to test the validity of wall thickening as a parameter of regional function. Regional morphology included wall thickness and radii of curvature measurements. With respect to transmural nonuniformity, subendocardial strains exceeded subepicardial strains. Going from base to apex, wall thickness and circumferential radii of curvature decreased, whereas longitudinal radii of curvature increased. All of the strains increased from LV base to apex, resulting in a higher ejection fraction (EF) at the apex than at the base (70.9 +/- 0.4 vs. 62.4 +/- 0.4%; means +/- SE, P < 0.0001). When we looked around the circumference of the ventricle, the anterior part of the LV was the flattest and thinnest and showed the largest wall thickening (46.6 +/- 1.2%) but the lowest EF (64.7 +/- 0.5%). The posterior LV wall was thicker, more curved, and showed a lower wall thickening (32.8 +/- 1.0%) but a higher EF (71.3 +/- 0.5%). The regional contribution of the LV wall to the ejection of blood is thus highly variable and is not fully characterized by wall thickening alone. Differences in regional LV architecture and probably local stress are possible explanations for this marked functional nonuniformity.     

Some implications of a constant fiber stress hypothesis in the diastolic left ventricle

A thick-wall incompressible, elastic sphere was used as a model for the diastolic rat left ventricle. A model for myocardial nonhomogeneity was derived assuming that fiber (circumferential) stress was independent of position in the ventricular wall. The theoretical implications of the resulting constitutive relations together with the spherical model were analyzed in the context of large deformation elasticity theory. It was found that muscle stiffness at a given level of uniaxial stress increased monotonically from the endocardium to the epicardium. In addition, fiber stress was found to be essentially a linear function of transmural pressure above a pressure of 6 g/cm². It was also shown theoretically that neglecting the nonhomogeneity of the myocardium resulted in a state of stress which differed significantly from that predicted by the nonhomogeneous model. For example, at a transmural pressure of 14 g/cm², fiber stress in the nonhomogenous model was equal to 17 g/cm² while fiber stress in the homogeneous model varied between 100 g/cm² at the endocardial surface and 2 g/cm² at the epicardial surface. The change in muscle stiffness with position which characterized the nonhomogeneous model also tended to linearize the highly curvilinear radial stress distribution predicted by the homogeneous model at a given transmural pressure.     

Simvastatin reverses cardiac hypertrophy caused by disruption of the bradykinin 2 receptor

Bradykinin 2 receptor (B2R) deficiency predisposes to cardiac hypertrophy and hypertension. The pathways mediating these effects are not known. Two-month-old B2R knockout (KO) and wild-type (WT) mice were assigned to 4 treatment groups (n = 12-14/group): control (vehicle); nitro-l-arginine methyl ester (l-NAME) an NO synthase inhibitor; simvastatin (SIM), an NO synthase activator; and SIM+l-NAME. Serial echocardiography was performed and blood pressure (BP) at 6 weeks was recorded using a micromanometer. Myocardial eNOS and mitogen-activated protein kinase (MAPK, including ERK, p38, and JNK) protein expression were measured. Results showed that (i) B2RKO mice had significantly lower ejection fraction than did WT mice (61% +/- 1% vs. 73% +/- 1%), lower myocardial eNOS and phospho-eNOS, normal systolic BP, and higher LV mass, phospho-p38, and JNK; (ii) l-NAME increased systolic BP in KO mice (117 +/- 19 mm Hg) but not in WT mice and exacerbated LV hypertrophy and dysfunction; and (iii) in KO mice, SIM decreased hypertrophy, p38, and JNK, improved function, increased capillary eNOS and phospho-eNOS, and prevented l-NAME-induced LV hypertrophy without lowering BP. We conclude that disruption of the B2R causes maladaptive cardiac hypertrophy with myocardial eNOS downregulation and MAPK upregulation. SIM reverses these abnormalities and prevents the development of primary cardiac hypertrophy as well as hypertrophy secondary to l-NAME-induced hypertension.